ae86 racecar with beams engine

[totta Crolla]

Not only are harmonic dampers necessary but they are also engine type specific being "tuned" to to the crankshaft.
If the pulley that was removed was a damper type and some are not, then you would be well advised to re-use it after careful checking of the rubber.
Why do you think Toyota put the rubber there in the first place ?

I'm sure if you do an internet search you will find more info on this.